The 2+2 Forums Older Archives: Interesting formula (Shove EV)

When you're in the SB, and you have X BB for your stack, your shove EV w/ any given hand is easy to calculate if you know the range of hands your opponent will call with.
X= your stack size (in terms of BB, assume the BB has an equal stack or has you covered. If you have the BB covered, X = the size of the BB's stack)
C = Percent of the time you are called
W = Percent of the time you win when you're called (use poker stove to figure this out)

Your EV is then:
(1-C)1.5 + WC(X+.5) - C(1-W)(X-.5)
translated this is:
1-C = % of the time you are steal the blinds
1.5 = the amount you win when you steal the blinds

WC = the percent of time you are called and win
X+.5 = the amount you win when you are called and win

C(1-W) = the percent of time you are called and lose
X-.5 = the amount you lose when you are called and lose

This formula simplifies to:

SHOVE EV = 1.5 - C + CX (2W-1)
X= stack size
C = % of time you are called
W = % of time you win when you are called

Example: You have 32o in the SB, and your opponent will call you with 22+, 54+, 86+, T7+, J6+ Q2+ (the loose range of hands in MJ's article).

According to poker stove, 32o wins 31% of the time against this range of hands, therefore W=.31

This range of hands accounts for 64% of all hands (13 pocket pairs x 6 combinations)+ (48 non pair hands * 16 combinations) = 78+768 = 846 combinations.
846 / 1326 = .64
Note that 1326 = total # of combinations of hands.
C=.64

Let's say your stack size is 10x BB.
We now have X=10
C=.64
W=.31

SHOVE EV = 1.5 - C + CX (2W-1)
Shove EV w/ 32o and 10x BB = 1.5 - .64 + (.64)(10)(.62-1)
Shove EV w/ 32o and 10x BB = -1.572 x BB

Any ideas on how to make a formula that estimates your EV on the button? The fact that there are 2 players left to act makes it much tougher.

I'm not sure how many applications there are for this formula, but I find this stuff interesting nonetheless.

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-Justin Bonomo
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